Arduino ethernet shield w 5100 and wifi network

Hello.I have arduino and ethernet w5100 shield with sd card and control my a/c.Can be converted to wireless to communicate with the modem router without network cable?With wifi shield?Thanks.

Maybe i must connect arduino and w5100 with modem via cable (work as webserver) and connect extra wifi shield for communication with other arduinos wifi who control my a/c...network wifi.I control my a/c via web.http://webgsmremotecontrol.webs.com.Any other ideas?

You could use a little WiFi router that you can cponnect directly to the Ethernet card that you already have.
Here in the US you ca get a TP-Link TL WR702n (or 702 or 3020......) viia a short Ethernet cable directly to the Ethenet card.
Then you can connect that in client (bridge) mode to the Modem-Router.

this is less expensive than buying a separate WiFi shieled and simple to set up without the need to re-write code.

Yes...this is good idea for control 1 device if i want to control multiple devices for all building?Example 6 a/c or thermostat(relay) can i create wi fi network?

Maybe is better with power RF T/R module...for wireless local communication inside home?

To control something as simple as Air Conditioning units you may want to use a different approach than WiFi.
Maybe X-Bee RF.